A Novel 1-Dimensional Cosine Chaotic Equation and Digital Image Encryption Technique

Abstract

In the 21st century, the digital era, chaotic systems become the backbone in designing the secure ciphers for image cryptography because of their intrinsic features like dynamical behavior and sensitivity to initial conditions. In this regard, 1-dimensional (1D) non-linear dynamical systems are one of the most studied in chaos theory. Besides the advantages of 1D chaotic systems, these systems have short periods and a short range of control parameters. A new 1D chaotic system called as Cosine Chaotic Equation (CCE) was developed to address this issue. The new and simple chaotic system has a larger range of control parameters $\alpha $ which increases the key space to make brute force attacks infeasible. The system is rigorously tested using the randomness evaluation metrics SP800-22 test suite recommended by the National Institute of Standards and Technology (NIST). It proved itself as an excellent addition in the pool of 1D chaotic systems to use safely in designing new ciphers. The new dynamical system is applied in an image encryption technique to prove its efficacy.

Keywords

• Cryptography
• pseudo-random number generator (PRNG)
• CCE
• chaos theory
• non-linear dynamical system
• image encryption